the null hypothesis is not rejected when it is false c.
Identify the critical value suitable for conducting a two-tail test of the hypothesis at the 2% level.
the research hypothesis is rejected when it is true d.
Any test of hypothesis has a risk associated with it and one is generally concerned with the or risk (a type I error which rejects the null hypothesis when it is true). The level of this α risk determines the level of confidence (1 – α) that one has in the conclusion. This risk factor is used to determine the critical value of the test statistic which is compared to a calculated value.
F distribution, which is a skewed distribution and is characterized by the degrees of freedom used to estimate S1 and S2, called the numerator degrees of freedom (n1 – 1) and denominator degrees of freedom (n2 – 1), respectively. Under the null hypothesis, the F statistic becomes S12/S22
the result would be unexpected if the null hypothesis were true c.
Would you reject the hypothesis H(0):MU = 69 versus the (one-sided) alternative H(1):MU > 69 on the basis of your observations, when testing at level ALPHA = .05?
Would you reject the hypothesis H(0):MU = 72 versus the alternative H(1):MU =/= 72 on the basis of the observations, when testing at level ALPHA = .05?
the null hypothesis is probably true d.
The fact that a hypothesis is consistent with a set of data does not mean that it is correct; whereas, if it is not consistent with the data set it may be incorrect.
This proce- dure can be viewed as a test of the hypothesis p = .05 against the alternative p > .05, p being the probability that the machine turns out a defective item.
reserve judgement about the hypothesis.
the null hypothesis is rejected when it is true.
Test the null hypothesis that the new ball does not improve a bowler's average at the 5% level of significance.
the result would be unexpected if the null hypothesis were true.
If we would reject a null hypothesis at the 5% level, we would also reject it at the 1% level.
The failure to reject does not imply the null hypothesis is true.
A hypothesis accepted at the ALPHA = .20 level of significance is probably true.
A number of commonly used hypothesis test terms are presented below.
We begin by considering hypothesis tests to compare parameters of a single population, such as , and fraction defective p, to specified values. For example, viscosity may be an important characteristic in a process validation experiment and we may want to determine if the population standard deviation of viscosity is less than a certain value or not. Additional examples of such comparisons are suggested by the following questions.
The sample size (n) needed for hypothesis testing depends on:
In the statistical inference discussion thus far, it has been assumed that the sample size (n) for hypothesis testing has been given and that the critical value of the test statistic will be determined based on the α error that can be tolerated. The ideal procedure, however, is to determine the α and β error desired and then to calculate the sample size necessary to obtain the desired decision confidence.
The null and alternative hypotheses are:
When the population follows a normal distribution and the population standard deviation, σx, is known, then the hypothesis tests for comparing a population mean, μ, with a fixed value, μ0, are given by the following:
Hypothesis | Definition of Hypothesis by Merriam …
The concept of power also relates to experimental design and analysis of variance.
The following equation briefly states the relationship for ANOVA.
1 – β = P(Reject H0 /H0 is false)
1 – β = Probability of rejecting the null hypothesis given that the null hypothesis is false.
Environmental Policy, R&D and the Porter Hypothesis in …
The above problems represent a comparison of a target or population variance with an observed sample variance, a comparison between several sample variances, or a comparison between frequency proportions. The standardized test statistic is called the Chi Square (χ2)test. Population variances are distributed according to the chi square distribution. Therefore, inferences about a single population variance will be based on chi square. The chi square test is widely used in two applications.
Case I. Comparing variances when the variance of the population is known.
Case ll. Comparing observed and expected frequencies of test outcomes when there is no defined population variance (attribute data).
When the population follows a normal distribution, the hypothesis tests for comparing a population variance, 0:, with a fixed value, 0:, are given by the following:
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